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Softa [21]
2 years ago
13

Find the equation of the line through point (10,4) and parallel to 3x+5y=8. Use a slash ("/") for fractions (e.g. 1/2 for 12). D

O not include spaces in your answers.
Mathematics
2 answers:
MAXImum [283]2 years ago
5 0

Answer:

3x + 5y = 50

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + 5y = 8 ( subtract 3x from both sides )

5y = - 3x + 8 ( divide terms by 5 )

y = - \frac{3}{5} x + \frac{8}{5} ← in slope- intercept form

with slope m = - \frac{3}{5}

Parallel lines have equal slopes , then

y = - \frac{3}{5} x + c ← is the partial equation

to fid c substitute (10, 4 ) into the partial equation

4 = - 6 + c ⇒ c = 4 + 6 = 10

y = - \frac{3}{5} x + 10 ← equation of parallel line in slope- intercept form

multiply through by 5 to clear the fraction

5y = - 3x + 50 ( add 3x to both sides )

3x + 5y = 50 ← equation of parallel line in standard form

Lyrx [107]2 years ago
5 0

Solution:

<u>Step-1: Convert the equation of the line into slope intercept form.</u>

  • 3x + 5y = 8
  • => 5y = -3x + 8
  • => y = -3x/5 + 8/5

In this case, the slope we obtained is -3/5, which is -0.6. Let's use point slope form to find the original equation.

<u>Step-2: Use point slope form.</u>

  • y - y₁ = m(x - x₁)
  • => y - 4 = -0.6(x - 10)
  • => y - 4 = -0.6x + 6
  • => y = -0.6x + 10
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